Time-dependent annealing and deposition on substrates with repulsive interactions

Abstract

In models of nucleation and growth of crystals on surfaces, it is often assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions and formulate the general time-dependent problem in a 2D potential field. We utilize the Master Equation Discretization(MED) method to solve the 2D time-dependent diffusion field of adparticles on general nonuniform (rectangular grid) substrates, and compare it against competing algorithms, including the FFT and hybrid-FFT methods previously introduced, for periodic boundary conditions. The physical context is set by the importance of repulsive interactions in the nucleation and growth of many nanostructures, e.g. metal nanoclusters, hut clusters and nanowires. The programs, realized in Matlab ® 6.5, are used to obtain quantitative capture numbers, aspect and direct impingement ratios, and other island growth quantities in the presence of potential fields, when particular surface processes are included. The case of no corner rounding is studied in detail. Strongly anisotropic potentials favor wire growth, which can be considerably influenced by alternate deposition and annealing, and the location of neighboring islands. Physical examples are given based on Ge/Si(001) material parameters.Essentially similar programs, differing only in outputs, are used to visualize the diffusion field and to produce realistic movies of crystal growth. Examples given here are linear deterministic calculations, but the framework allows for inclusion of non-linear and statistical effects for particular applications.

Mean-field theory of nucleation and growth on strained surfaces

“…The case of anisotropic but spatially constant D has already been studied. 14 Here, we extend this by a brief study of the effect of strain on island growth, with a more detailed study to follow. 15 The adparticle dynamics follows the continuum equation ͓Eq.…”

“…Timelapse movies have been made to visualize the growth processes, as MATLAB movies ͑mov͒ and video clips ͑avi͒. 14,15 The diffusion constant D and strain are both symmetric in position x, whereas the drift velocity v is antisymmetric; the case of ␣ 2 − ␣ 1 = 0.75 eV is highlighted, with the ␣ 2 = ␣ 1 case shown by the dotted line for comparison. Note that strain causes a 60% increase in the diffusion constant far away from the island and a much larger enhancement close to the island edges.…”

Conditions for organized nanoring growth using kinetic Monte Carlo simulations

“…Heteroepitaxy has been widely studied to define, through various models, [9][10][11][12][13][14][15][16][17] the conditions of formation of self-organized nanostructures regarding their number, size, shape, and chemical composition. Carefully controlling and monitoring the size and geometry of these structures generate specific electric, 18 optical, 19 and magnetic 20 properties.…”